{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HR4XMK6BR6Q75BUDU35ORTOGAY","short_pith_number":"pith:HR4XMK6B","schema_version":"1.0","canonical_sha256":"3c79762bc18fa1fe8683a6fae8cdc60638826a18f90bce803e8c4e710a5ba876","source":{"kind":"arxiv","id":"2606.23509","version":1},"attestation_state":"computed","paper":{"title":"Variance or Standard Deviation? Shell Geometry and Global-Scale Priors in High-Dimensional Shrinkage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM","stat.ML"],"primary_cat":"stat.ME","authors_text":"Wayne Yuan Gao, Zhiheng You","submitted_at":"2026-06-22T15:57:01Z","abstract_excerpt":"We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-po"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.23509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-22T15:57:01Z","cross_cats_sorted":["econ.EM","stat.ML"],"title_canon_sha256":"a6b95711499390ad89980e07f08183b6331b580dcb77afb755e996631cdf04c2","abstract_canon_sha256":"ab7506385ada7d277c9928145d6c180d9dd52527e29a5bcb1648f8f7a38e7c9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:21.875854Z","signature_b64":"EHnHQGdrCuSafLc9IozvqfIAFMuna3J8lWLy8vVY5r6LqtZvUlqOCwCvL6Wtk+EL405Lq26FA+E9/wtlhGfZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c79762bc18fa1fe8683a6fae8cdc60638826a18f90bce803e8c4e710a5ba876","last_reissued_at":"2026-06-23T03:14:21.875455Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:21.875455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variance or Standard Deviation? Shell Geometry and Global-Scale Priors in High-Dimensional Shrinkage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM","stat.ML"],"primary_cat":"stat.ME","authors_text":"Wayne Yuan Gao, Zhiheng You","submitted_at":"2026-06-22T15:57:01Z","abstract_excerpt":"We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23509","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23509/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.23509","created_at":"2026-06-23T03:14:21.875512+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.23509v1","created_at":"2026-06-23T03:14:21.875512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23509","created_at":"2026-06-23T03:14:21.875512+00:00"},{"alias_kind":"pith_short_12","alias_value":"HR4XMK6BR6Q7","created_at":"2026-06-23T03:14:21.875512+00:00"},{"alias_kind":"pith_short_16","alias_value":"HR4XMK6BR6Q75BUD","created_at":"2026-06-23T03:14:21.875512+00:00"},{"alias_kind":"pith_short_8","alias_value":"HR4XMK6B","created_at":"2026-06-23T03:14:21.875512+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY","json":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY.json","graph_json":"https://pith.science/api/pith-number/HR4XMK6BR6Q75BUDU35ORTOGAY/graph.json","events_json":"https://pith.science/api/pith-number/HR4XMK6BR6Q75BUDU35ORTOGAY/events.json","paper":"https://pith.science/paper/HR4XMK6B"},"agent_actions":{"view_html":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY","download_json":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY.json","view_paper":"https://pith.science/paper/HR4XMK6B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.23509&json=true","fetch_graph":"https://pith.science/api/pith-number/HR4XMK6BR6Q75BUDU35ORTOGAY/graph.json","fetch_events":"https://pith.science/api/pith-number/HR4XMK6BR6Q75BUDU35ORTOGAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/action/storage_attestation","attest_author":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/action/author_attestation","sign_citation":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/action/citation_signature","submit_replication":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/action/replication_record"}},"created_at":"2026-06-23T03:14:21.875512+00:00","updated_at":"2026-06-23T03:14:21.875512+00:00"}